Hardy Type Inequalities on Domains with Convex Complement and Uncertainty Principle of Heisenberg
- 作者: Avkhadiev F.1, Makarov R.1
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隶属关系:
- Kazan (Volga Region) Federal University
- 期: 卷 40, 编号 9 (2019)
- 页面: 1250-1259
- 栏目: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205447
- DOI: https://doi.org/10.1134/S199508021909004X
- ID: 205447
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详细
We prove new integral inequalities for real-valued test functions defined on subdomains of the Euclidean space. We assume that the complement of the subdomain is a non-empty convex set. We prove an extension of the Hadwiger theorems about approximations of convex compact sets by polytopes and obtain some generalizations and improvements of several Hardy type multidimensional inequalities. In particular, in the last section we present an improvement of a two-dimensional inequality, connected with the uncertainty principle of Heisenberg.
作者简介
F. Avkhadiev
Kazan (Volga Region) Federal University
编辑信件的主要联系方式.
Email: avkhadiev47@mail.ru
俄罗斯联邦, Kazan, 420008
R. Makarov
Kazan (Volga Region) Federal University
编辑信件的主要联系方式.
Email: ruva2007@yandex.ru
俄罗斯联邦, Kazan, 420008